BGE no shadows with GLSL
Baking

Baking is a process to generate textures. The texture is build from different camera views. To be more specific a camera gets placed above a face, renders the image and applies the result to a new texture.

This way you get render effects into your texture. E.g. you do not need dynamic shadows, so you can "bake" them into the final texture. It looks like there are shadows, but they are not. This saves a lot of processing power.

Situation

While you can use baked textures it does not apply to your situation. You have textures already. 

The problem you have is that your materials are not completely set up. GLSL uses the material and texture settings (see the according tabs in the property view). Multi-texture uses whatever texture you assigned in UV-Editor.

This means when you want to see your scene in GLSL, you need to apply the textures via texture tab. The Multitexture mode likes it as well.